Question: What do the following two equations represent? $-4x+5y = 3$ $-20x+25y = 3$
Solution: Putting the first equation in $y = mx + b$ form gives: $-4x+5y = 3$ $5y = 4x+3$ $y = \dfrac{4}{5}x + \dfrac{3}{5}$ Putting the second equation in $y = mx + b$ form gives: $-20x+25y = 3$ $25y = 20x+3$ $y = \dfrac{4}{5}x + \dfrac{3}{25}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.